Digital Signal Processing
24. Digital Signal Processing
Academic and Research Staff
Prof. A.V. Oppenheim, Prof. A.B. Baggeroer, Prof. J.S. Lim, Prof. B.R. Musicus,
Dr. D.R. Mook, Dr. J.C. Lee
Graduate Students
T.E. Bordley, P. Chan, S.R. Curtis, D.S. Deadrick, W.P. Dove, F.U. Dowla,
M_ Feder, D.W. Griffin, W.A. Harrison, W. Huang, D. lzraelevitz, P. Kenny, D.M.
Martinez, E.E. Milios, C. Myers, T.N. Pappas, M.D. Richard, H. Sekiguchi,
R. Sundaram, P.L. Van Hove, M.S. Wengrovitz, A. Zakhor
24.1 Introduction
The Digital Signal Processing Group is carrying out research in the general area of signal
processing.
In addition to specific projects being carried out on campus, there is close
interaction with Lincoln Laboratory, and with the Woods Hole Oceanographic Institution. While a
major part of our activities focus on the development of new algorithms, there is a strong
conviction that theoretical developments must be closely tied to applications. The application
areas which we currently are involved with are speech, image, video and geophysical signal
processing.
We also believe that algorithm development should be closely tied to issues of
implementation since the efficiency of an algorithm depends not only on how many operations it
requires, but also on how suitable it is for the computer architecture it runs on.
Also strongly
afiecting our research directions is the sense that while historically signal processing has
principally emphasized numerical techniques, it will increasingly exploit a combination of
numerical and symbolic processing, a direction that we refer to as knowledge-based signal
processing.
In the area of speech processing, we have, over the past several years, worked on the
development of systems for bandwidth compression of speech, parametric speech modeling,
time-scale modification of speech and enhancement of degraded speech. Recently, based on a
general class of algorithms involving the estimation of a signal after its short-time Fourier
transform has been modified, we have dCveloped a very high quality system for time-scale
-liable pitch dnt-ection. We are nlso exploring
modific'ation of sp-eech and also a system for vry rty
now techniques for speech enhancement using adaptive noise cancelling when multiple
microphones
are available.
Speech processing is also the basis for two projects on
knowledge-based signal processing.
artificial i
One combines signal processing with the concepts of
and expert systems in the dement of a knowledge-based pitch detector, and
Intellige.nce
the second the development of a system for knowledge -based
165
speech modeling and
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enhancement.
In image processing, we are pursuing a number of projects on restoration, enhancement, and
coding. One project is restoration of images degraded by additive noise, multiplicative noise, and
convolutional noise. Our current work in this project involves development of a new approach to
adaptive image restoration based on a cascade of one-dimensional adaptive filters. This
approach, when applied to some existing image restoration systems, not only reduces the number
of computations involved but improves the system performance. Another project we are currently
exploring is the development of a very low bit-rate (below 50 Kbits/sec) video-conferencing
system. The specific approach we are studying involves the transformation of an image into a
one-bit intensity image by adaptive thresholding and then coding the one-bit intensity image by
run-length coding. In addition, we are currently working on algorithm development for detection
and identification of artificial objects in infrared radar images. In this project, we hope to
incorporate both signal processing and artificial intelligence techniques, and hope to exploit both
the intensity and range map information.
In the area of geophysical signal processing, there are a variety of ongoing and new projects.
Work on determining characteristics of the ocean bottom by inverting a measured acoustic field is
continuing, and associated with this, we continue to explore algorithms for evaluating Hankel
transforms, and are investigating new field migration algorithms. Also, there are a number of
projects related to a series of major experiments in the eastern Arctic in 1980 and 1982, and to a
series of experiments in the marginal ice zone of the Arctic in 1983 and 1984. These projects
include examining the properties of several velocity function inversion techniques for
multi-channel ocean-bottom interaction data and extending the parabolic wave equation
approximation for modeling underwater acoustics. Also of potential importance to geophysical
signal processing is our work on knowledge-based signal processing with distributed sensor
nets, being carried out in collaboration with Lincoln Laboratory.
There are also a number of projects directed at the development of new algorithms with broad
potential applications. For some time we have had considerable interest in the broad question of
signal reconstruction from partial information, such as Fourier transform phase or magnitude. We
have shown theoretically how under very mild conditions signals can be reconstructed from
Fourier transform phase information alone. This work has also been extended to reconstruction
of multidimensional signals from one bit of phase, and, exploiting duality zero-crossing and
threshold crossing information. We have also developed a variety of theories and algorithms
relating to signal reconstruction from Fourier transform magnitude and from partial short-time
Fourier transform information. We are also exploring the application of some of these theoretical
results to problems such as speech and image coding. We have also obtained significant results
and continue to explore new algorithms for high-resolution multidimensionai spectral estimation.
Recently, we have also proposed a new approach to tPe problem of estimating multiple signal
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Digital Signal Processing
and/or parameter unknowns using incomplete and noisy data.
Our Minimum Cross-Entropy
Method applies an information theoretic criterion to optimally estimate a separable probability
density for the signal model. Not only does this new approach include all the various Maximum
Likelihood and Maximum A Posteriori methods as degenerate cases, but it also directly leads to a
simple iterative method of solution in which we alternate between estimating the various
unknowns, one at a time. We are now exploring applications to statistical problems, iterative
signal reconstruction, short-time analysis/synthesis, and noisy pole/zero estimation.
With the advent of VLSI technology, it is now possible to build customized computer systems of
astonishing complexity for very low cost. Exploiting this capability, however, requires designing
algorithms which not only use few operations, but also have a high degree of regularity and
parallelism, or can be easily pipelined. Directions we are exploring include systematic methods
for designing multi-processor arrays for signal processing, isolating signal processing primitives
for hardware implementation, and searching for algorithms for multi-dimensional processing
which exhibit a high degree of parallelism.
24.2 Improved Paraxial Methods for Modeling Underwater
Acoustic Propagation
U.S. Navy - Office of Naval Research (Contracts N00O 14-8 1-K-0742 and N00014-77-C-0266)
Arthur B. Baggeroer. Thomas E. Bordley
Current paraxial techniques for modeling wave propagation in the ocean perform poorly when
bottom interaction is important, due to their inability to handle wide-angle propagation.
Such
methods solve a simplified form of the wave equation, obtained by splitting the field into
transmitted and reflected components, and then neglecting the reflected field. In spite cf their
poor performance, the fundamental assumption underlying these techniques remains true: the
energy transmitted forward greatly dominates the energy reflected back; so modeling the
transmitted field alone should suffice. The concern of this work is to develop paraxial methods
less restricted in angle, yet retaining the numerical stability and efficiency which have made this
class of solutions so valuable. The approach taken is to generalize the notion of a split to allow
variation in range and depth, and to define a measure of the consistency of the split in term of the
observed field alone.
The algorithm studied generates the field iteratively using the current
estimate of the field to generate the split for the next step by requiring that the new split be
coIIl
stenI L Vwithlthe oubuserved filU.
The effectiveness of thi1I
approach is examined in the context
of modeling sound propagation in the Arctic Marginal Ice Zone.
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24.3 Signal Reconstruction from Fourier Sign Information
U.S. Navy - Office of Naval Research (Contract NOO014-81-K-0742)
National Science Foundation (Grants ECS80-07102 and ECS84-07285)
Alan V. Oppenheim, Susan R. Curtis
In a variety of applications, it is necessary or desirable to recover a signal from the knowledge of
the location of its zero crossings or from sign information. One such application occurs when a
signal is clipped or otherwise distorted in such a way as to preserve the zero crossing or level
crossing information, and it is desired to recover the original signal. Another application occurs
in the theory of vision where studies have stressed the importance of edge detection as a means
of classifying and identifying images but have not succeeded in developing a strong theoretical
basis for this work. A third application occurs in some design problems where one might want to
specify a filter response or antenna pattern in terms of zero crossing or null points (such as for
interpolation) and derive the remainder of the response from these.
We have developed new theoretical results on reconstruction of multidimensional signals from
sign information in either the Fourier or signal domain. Specifically, we have developed a set of
conditions under which a broad class of multidimensional signals are uniquely specified by the
sign of the real part of the Fourier transform. The problem of reconstruction from the zero
crossings of the original signal is a dual to this problem since it involves recovering a signal from
s ign inform.ation in the signal domain rather than i the Fourier domain. We have also extended
these results to permit reconstruction from crossings of an arbitrary threshold rather than just
zero crossings.
In addition to developing conditions under which a signal is uniquely specified with zero
crossings, we have also worked on developing practical algorithms for reconstructing signals
from this information.
We have applied two algorithms previously used in other signal reconstruction problems to the
problem of reconstruction from zero crossings. One of these algorithms involves solving a set of
linear equations and the other involves an iterative procedure imposing different constraints in
the space and frequency domains. We have successfully recovered a number of example images
from zero crossings but more research is needed in this area.
We are also interested in finding new applications of our results. It is tempting to consider the
application of these results to developing a low bit rate coding scheme which might involve
transmitting the sign information alone or the zero crossing locations and recovering the original
signal from these. In practice, however, recovery of the original signal is very sensitive to knowing
the exact zero crossing locations and it is difficult to achieve good results even with very small
errors in the zero crossing locations. We are currently exploring other applications of our results,
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Digital Signal Processing
including filter design and sampling theory.
24.4 Knowledge-Based Pitch Detection
Amoco Foundation Fellowship
National Science Foundation (Grants ECS80-07102 and ECS84-07285)
U.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)
Sanders Associates, Inc.
Alan V. Oppenheim, Randall Davis, Webster P. Dove
Knowledge-based signal processing is an effort to design signal processing programs that go
beyond purely numerical processing of the data and try to symbolically reason about the problem
in order to better solve it. Problems appropriate for this area are those whose model is either too
complex to be solved directly with a numerical algorithm, and those for which the model is not
well understood.
Pitch detection falls into this category both because the speech signal model is not well
specified, and because the model for the generation of pitch is not fully understood.
This project is developing a program called the Pitch Detector's Assistant (PDA) which will both
serve to reduce the effort involved in generating hand edited pitch and provide a laboratory for
studying and programming the knowledge that makes humans better pitch trackers than existing
automatic algorithms.
1
Existing methods of semi-automatic pitch detection require the user to make a voicing
decision and select a pitch individually for every frame. The PDA program is intended to analyze
as much of the utterance as it is sure of and then help the user with the remaining difficult
portions. Thus we expect a dramatic reduction in the time from the current 30 minutes per
second of speech analyzed.
Although there have been projects which combine signal processing and Al technology for
2.3
and underwater acoustic signal
particular problems such as speech understanding
recognition, 4 the actual signal processing present in these systems has only been used as a
means for generating symbolic objects. These objects are then manipulated by the Al portions of
the program until an interpretation of the data is complete.
The symbols do not provide
information to assist subsequent nunmerical processing, and thus the information flows one way
from numeric to symbolic form. The pitch detection problem choice is motivated by the
observation that these other probhlems are ones of recognition (i.e. signals in, symbols out) and
naturally lead to solutions which process numIericaily first and symbolically later.
By choosing a problem vwhich involves signal output we assure the use of numerical processing
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in later portions of the program. The creation and study of programs which emphasize the
interaction between symbolic and numerical processing, is the primary purpose of the
knowledge-based signal processing effort at M.I.T.
References
1. C.A. McGonegal, L.R. Rabiner, and A.E. Rosenberg, "A Semiautomatic Pitch Detector
(SAPD)," IEEE Trans. ASSP 23, 570-574, December 1975.
2. L. Erman, R. Hayes-Roth, V.R. Lesser, and D.R. Reddy, "The Hearsay-II Speech Understanding
System: Integrating Knowledge to Resolve Uncertainty," Computing Surveys 12, 213-254,
June 1980.
3. B. Lowerre and R. Reddy, "The HARPY Speech Understanding System," in W. Lea (Ed.),
Trends in Speech Recognition (Prentice-Hall, Englewood Cliffs, New Jersey 1980), pp.
340-360.
4. H.P. Nii, E.A. Feigenbaum, J.J. Anton. and A.J. Rockmore, "Signal-to-Symbol Transformation:
HASP/SIAP Case Study," Al Magazine 3, 23-35, Spring 1982.
24.5 Bearing Estimation of Wideband Signals by
Multidimensional Spectral Analysis
U.S. Navy - Office of Naval Research (Contract N00014-8 1-K-0742)
National Science Foundation (Grant ECS80-07102)
Jae S. Lim, Farid U. Dowla
Directions of a stationary and homogeneous wvefield is conventionally determined by the
frequency-wavenumber method. While the frequency-wavenumber method is useful in many
applications, for bearing estimation of wideband planewaves of unknown temporal spectra and
velocities, the computation of the frequency-wavenumber method may be unwarranted in view of
the proposed spatial approach. The proposed approach is based on estimating the zero--delay
covariance function, the time-space covariance function of the wavefield evaluated only at the
zero
temporal
lag.
Just
as
the
cross-spectral
covariance
function
determines
a
frequency-wavenumber spectrum, the zero-delay covariance function determines a zero-delay
wavenumber spectrum, the spatial spectrum of the wavefield. The underlying theoretical basis of
the proposed approach is that for a planar array the zero-delay wavenumber spectrum can be
used to determine the bearings of the planewave sources. Unlike the frequency-wavenumber
method which attempts to resolve sources at a single frequency, the proposed method attempts
to resolve multiple sources at different frequencies in the spatial spectrum at once. Both the
freq ency-wavenumber and the propPosed mthod utili7e multidimensional spectral estimation
algorithms to obtain the spatial spectrum.
For a finite aperture array, the operation of a
high-resolution wavenumber estimation method is important for separating the planewave
sources in bearing. A new high-resolution spectral estimation method with useful computational
property is introduced.
This algorithm may be used either with the zero-delay covariance
function or with the cross-spectral covariance function.
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This work was compl7-ted in November.
24.6 The Estimate-Maximize(E-M) Algorithm and its
Application to Signal Processing Problems
National Science Foundation (Grant ECS84-07285)
U.S. Navy - Office of Nc-val Research (Contract N00014-81-K-0742)
Alan V. Oppenheim, Me ir Feder
In many signal processing problems one has to estimate unknown parameters. Usually this is
done using the Maximum Likelihood (ML) criterion. Unfortunately, sometimes the parameters are
connected to the observed signal in a complicated way and so maximizing the likelihood function
is not an easy task.
The Estimate-Maximize (E-M) algorithm, 1 is an iterative algorithm that converges to the ML
solution. We assume that there is an extension of the observations for which the ML estimate of
the parameters is simple. We will call that extension "complete data". At each iteration we first
estimate the sufficient statistics of the complete data given the observed signal and the previous
values of the parameters (Estimate E-Step) and then get the new values of the parameters by
maximizing the likelihood function of the complete data where we substitute the estimated
statistics instead of observed sufficient statistics (Maximize M-step).
Some examples of signal processing problems for which this idea is natural are:
* Parametric spectrum estimation from short data - the complete data will be a large
data record.
* Signal parameters estimation when the signal is corrupted by noise - the complete
data will be the signal alone and the noise alone.
* Array processing problems :
(i) multiple sources problem - the complete data will be
each source separately
(ii) multipath problem - the complete data will be each path
separately
kill) LIIIIe delay estitldl
UIIon -- the comII
lete Ud d will Utbe a
large record for which the generalized cross correlator is optimal.
In this research we will try, on one hand. to find genera! properties of the E-M algorithm like
convergence rate, adaptive versions, deterministic versions, etc., and on the other hand, to carry
out the algorithm experimentally on some of ;he above problems and to establish this algorithm as
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a procedure for solving those signal processing problems.
References
1. A.P. Dempster et al., "Maximum Likelihood from Incomplete Data via the EM Algorithm," Ann.
of Royal Stat. Soc. (1977), pp.1-38.
24.7 Speech Synthesis from Short-Time Fourier Transform
Magnitude Derived from Speech Model Parameters
National Science Foundation (Grants ECS80-07102 and ECS84-07285)
Sanders Associates, Inc.
U.S. Navy - Office of Naval Research (Contract N00014-8 1-K-0742)
Jae S. Lim, Daniel W. Griffin
Previous approaches to the problem of synthesis from estimated speech model parameters
have primarily employed time-domain techniques. Most of these methods generate an excitation
signal from the estimated pitch track. Then, this excitation signal is filtered with a time-varying
filter obtained from estimates of the vocal tract response. This approach tends to produce poor
quality "synthetic" sounding speech.
In this research, a new approach to speech synthesis from the same estimated speech model
parameters is investigated. In this approach, a desired Modified Short-Time Fourier Transform
Magnitude (MSTFTM) is derived from the estimated speech model parameters. The speech
model parameters used in this approach are the pitch estimate, voiced/unvoiced decision, and
the spectral envelope estimate. The desired MSTFTM is the product of a MSTFTM derived from
the estimated excitation parameters and a MSTFTM derived from spectral envelope estimates.
(The word "modified" is included in MSTFTM in these cases to emphasize that no signal exists, in
general, with this MSTFTM.) Then, a signal with Short-Time Fourier Transform Magnitude
(STFTM) close to this MSTFTM is estimated using the recently developed LSEE-MSTFTM
algorithm. 1'2 Preliminary results indicate that this method is capable of synthesizing very
high-quality speech, very close to the original speech.
This method has applications in a number of areas including speech coding and speech
enhancement. In speech coding applications, the excitation parameters and spectral envelope
can be coded separately to reduce transmission bandwidth. Then, these coded parameters are
LI
ransILLUU clZU U en decoded and reco bined at the receiver. in speech eniianement
applications, the excitation parameters and the spectral envelope can be separated, processed
separately, and then recombined.
References
1. D.W. Griffin and J.S. Lim, "Signal Estimation from Modified Short-Time Fourier Transform,"
Proceedings of the 1983 Int. Conf. on Acoustic_,_ Speech and Signn Processing, Boston,
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Massachusetts, April 14-16, 1983, pp.804-807.
2. D.W. Griffin and J.S. Lim, "Signal Estimation from Modified Short-Time Fourier Transform,"
IEEE Trans. Acoust., Speech, Signal Process., ASSP-32, 2, 236-243, April 1984.
24.8 Reconstruction of a Two-dimensional Signal from its
Fourier Transform Magnitude
National Science Foundation (Grants ECS80-07702 and ECS84-07285)
U.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)
Jae S. Lim, David lzraelevitz
In a wide range of applications, such as radio astronomy, crystallography, and holography, it is
of great interest to reconstruct an unknown signal from measurements of the magnitude of its
Fourier transform. Some progress has been made in the area in recent years. The uniqueness of
the reconstruction has been proven for a large family of signals; specifically, all those
two-dimensional signals with a non-factorable z-transform. In addition, several algorithms have
been proposed for the reconstruction of the signal.
Unfortunately, none of the proposed
algorithms are guaranteed to converge to the true solution. It is encouraging to note, however,
that much progress has been made lately in the related fields of reconstruction from various
amounts of phase and magnitude information.
In this research we are considering several new approaches to the problem of signal
reconstruction from Fourier transform magnitude. Our purpose is to incorporate recent research
results to develop an algorithm for reconstruction from Fourier transform magnitude which will be
guaranteed to yield a solution as long as the underlying signal satisfies the conditions for
uniqueness.
24.9 Motion Compensated Noise Reduction for Motion Video
Scenes
Advanced Television Research Program
National Science Foundation (Grants ECS80-07102 and ECS84-07285)
U.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)
Jae S. Lim, Dennis M. Martinez
Signals which correspond to motion video scenes possess a great deal of spatial and temporal
redundancy. Many image processing algorithms exploit the spatial redundancy in one form or
another. However, when dealing with 3-D signals generated from motion video scenes, there is
also a significant amount of temporal redundancy among adjacent image frames. In fact, often
the only changes in the scene from one frame to the next are those iritroduced by motion within
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the scene. By properly identifying the relevant motion trajectories of the objects within a scene,
motion information can be used in various image processing problems.
This research is concerned with two fundamental issues. The first issue involves investigating
techniques for performing motion estimation given a set of noisy image frames. Basically, the
problem is to estimate the displacement field in those regions of the scene where motion is
present. The displacement field is a 2-D vector field, which is the function of the two spatial
coordinates and the temporal coordinate, that describes the motion trajectories. The second
issue is to develop algorithms which can incorporate motion information for the purpose of noise
reduction. Filters which incorporate motion information exploit the temporal redundancy of these
signals, and should theoretically permit greater signal-to-noise improvements than are possible
using only spatial information.
24.10 Knowledge-Based Harmonic Source Detection and
Direction Determination
National Science Foundation (Grants ECS80-07102 and ECS84-07285)
Sanders Associates, Inc.
U.S. Navy - Office of Naval Research (Contract N00014-8 1-K-0742)
Alan V. Oppenheim, Evangelos E.Milios
Architectural and design issues in knowledge-based signal processing are examined in the
context of acoustic waveform processing for harmonic source detection and direction
determination. The system under construction takes as input a set of noisy acoustic waveforms
and produces hypotheses about the existence and direction of harmonic sound sources present
in tile waveforms. The approach
processing
using
techniques
combines signal
from
derived
processing and symbolic information
domain
the
of
artificial
intelligence
and
knowledge-based systems. The system uses signal processing operators as probing tools and
has the capability of interpreting the results of their application and of constructing concise
symbolic descriptions of waveform features. A unique aspect of the system is that it fully
integrates signal processing and symbolic processing, as opposed to previous systems, which
used signal processing as a simple front end. In the system under construction, the problem of
planning the application of a variety of signal processing operators is posed and it is handled by
applying knowledge about the operators based on past experience. The mechanism for
.-
IUorm lizing the relevant
. ..
rknowledge
l
..
is that
....
.
.
..
,.. . ~,...c
...
b..L
:
t.
flprouoco Uadalysis, datechnique by which a person
with experience in processing acoustic data is given particular problems to solve and all his
actions, as well as the related reasoning, are recorded and analyzed. Particular rules are
extracted from this analysis, which also dictates the overall system architecture. The system is
being implemented in a rule language implemented in LISP and uses a highly modular signal
processing package also in LISP.
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Digital Signal Processing
The work is being done in collaboration with the Distributed Sensor Netwvorks program at M.I.T.
Lincoln Laboratory.
24.11 Knowledge-Based Speech Analysis and Enhancement
Amoco Foundation Fellowship
National Science Foundation (Grants ECS80-07102 and ECS84-07285)
Sanders Associates, Inc.
U.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)
Alan V. Oppenheim, Cory Myers
The problems of speech modeling and speech enhancement for speech degraded by noise are
ones which have been of great interest in the signal processing community. As part of our efforts
to explore methods by which signal processing and symbolic processing techniques can be made
to interact, we are building a system for symbolic reasoning about speech analysis and
enhancement. For analysis, the system produces a time-varying parametric model of the speech
signal where, not only do the parameters change over time, but the models used may also change
over time. For example, the system may perform all-pole modeling of the signal but may change
the number of poles which are to be used in different portions of the signal. The system attempts
to develop a parametric model of a speech signal given both the speech signal (or a noisy version
of it) and a symbolic description of how the signal was produced. The symbolic description of the
signal includes information about the speaker, such as gender and age, and information about
the recording environment, such as noise characterization, sampling rate and speech bandwidth.
The system is also given a symbolic description of the content of the signal in the form of a
time-aligned phonetic transcription.
The output from the analysis portion of the system is a
time-varying parametric representation of the speech signal (excluding excitation information).
For speech enhancement the system takes the parametric representation generated from the
analysis section and combines it with classical speech synthesis techniques in order to enhance
the signal when noise is present. The system combines three different techniques in order to
produce an enhanced version of the noisy speech signal. In those regions of the signal where the
system can be expected to do a reasonable job of speech modeling in spite of noise and where
the measured parameters are reasonable in the context of the known symbolic information the
system does resynthesis from the measured parameters. In those regions of the signal where the
system fIails comipletely to measure reasonable speech parameters the system uses a phoneme to
speech synthesis system., n those regions where come measurements can be made reliably (but
not all measurements can be made reliably) the system uses the good measurements to infer the
unknown information. For example, the system may guess the third formant given the first and
second forrnants and the identity of the phoneme.
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Digital Signal Processing
The system is structured as an Expert System. This approach to system building emphasizes
the knowledge used to solve a problem and tries to make this knowledge explicit in the system.
Both phonetic knowledge and signal processing knowledge are represented in this way. The
signal processing and symbolic processing interact closely, with the signal processing driving the
symbolic processing in some cases and the signal processing being driven by the symbolic
processing in other cases.
24.12 Estimation of the Degree of Coronary Stenosis Using
Digital Image Processing Techniques
National Science Foundation (Grants ECS80-07102 and ECS84-07285)
U.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)
Jae S. Lim, Thrasyvoulos N. Pappas
The aim of this research is the development of a new algorithm for evaluating the degree of
coronary artery stenosis from coronary angiograms.
An angiogram is an x-ray picture of the
coronary arteries in which a contrast agent has been injected via a catheter. The precise and
objective measurement of the stenosis of the coronary arteries is important in the treatment of
patients with ischemic heart disease.
The techniques for quantifying the stenosis of the coronary arteries are similar to those used for
stenosis determination of other arteries like the femoral and carotid. However, due to the location
of the coronary arteries on the beating heart and their shape and size, their x-rays are very
difficult to obtain and analyze. The performance of existing techniques is not satisfactory when
they are applied to coronary arteries.
Coronary artery stenosis is determined as the maximum percent arterial narrowing within a
specified length of the vessel.
This requires the detection of the boundaries of the coronary
arteries and the analysis of the variation of their diameter. Current algorithms find the boundaries
of the artery as those points along a series of lines perpendicular to the vessel image where the
film density change is maximum.
We will consider a different approach. We will construct a
parametric model of the film density along the lines perpendicular to the vessel image, and based
on the observed density values we will estimate the parameters at each perpendicular line along
the vessel. The parameters of our model will include the vessel diameter and centerpoint and will
,C.cnount for the structure of the bacrkground (e g, varriation in soft tiie
thickness, presence of
bones, the diaphragm, etc.) as well as the distortions introduced by the imaging system.
Since our estimation procedure will use more information about the blood vessels than just the
maxirnum slope points of the film density at each perpendicular line, we expect it to have a better
performance than the present methods. Preliminary results show that the estimation of the blood
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Digital Signal Processing
vessel boundaries based on such a parametric model is at least as good as that of the other
methods.
The continuity of the vessel parameters as we move from line to line, which follows from the
spatial continuity of the vessel, will also be incorporated into our model and is expected to
significantly improve the accuracy of our estimation procedure.
We plan to test our algorithm both on real coronary angiograms and on x-rays of contrast
medium filled cylindrical phantoms obtained over a wide range of radiographic conditions. The
latter will provide information about the distortion introduced by the imaging system, and will
enable us to compare our computer-derived measurements of the phantom diameters with their
known values.
24.13 Low Bit Rate Video Conferencing
M.I. T. Vinton Hayes Fellowship
National Science Foundation (Grant ECS80-07102)
U.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)
Jae S. Lim, Ramakrishnan Sundaram
The attempt of this research is to achieve a drastic reduction in the channel capacity
?es
requi,e,
f
video transmissions.
An algorithm based on local averaging and adaptive
thresholding has been developed which reduces an 8-bit picture to a 1-bit binary picture without
significant loss in quality. The resulting image is then smoothed by adaptive median filtering to
remove random bit transitions. This is then suitable for run length coding. Compression factors
of Lip to 60 are expected to result. Other forms of data encryption are also being examined.
Currently the emphasis is only on intraframe redundancy reduction. The work is expected to lead
to interframe analysis.
24.14 The Curvature Spherical Image, a New Representation
of 3-D Objects
National Science Foundation (Grants ECS80-07102 and ECS84-07285)
U.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)
Jae S. Lim, Patrick Van Hove
This research addresses the relationships between an object and the boundaries of its
silhouettes, which will be referred to as contours, corresponding to various three--dimensional
(3-D) orientations of the line of sight. For this purpose, special models of objects and silhouettes
are considered. The property sphere of an object is defined on a unit sphere which is related to
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the object by a 3-D Gaussian mapping. Similarly, the property circle is related to the contour it
represents by a 2-D Gaussian mapping. In earlier computer vision work, property spheres and
circles have been used independently, and their applications have been limited to the
representation of scalar fields of object properties.
In a first stage, we have shown how the concepts of property spheres and circles can be
usefully combined to relate the properties of an object and those of its contours. Specifically, it is
proved that a slice through the property sphere of an object leads to the property circle of the
contour corresponding to the line of sight perpendicular to that slice.
In a second stage, a new concept of object modeling has been introduced, where the property
sphere is used as a domain for vector and tensor fields of object properties. In particular, a new
representation of 3-D objects, referred to as the Curvature Spherical Image (CSI), maps the
curvature tensor field of the surface of an object on its property sphere. The key advantage of
this representation is that a slice through the CSI and a subsequent projection of the tensor field
onto the slice produces the Curvature Circular Image (CCI) of the contour corresponding to the
line of sight perpendicular to the slice. The CCI itself is a mapping of the radius of curvature
scalar field of a contour on its property circle.
The study now progresses with attempts to use these new concepts in the matching of 2-D
contour measurements with 3-D object models. An issue which will be addressed in the course of
the research is the modelling of convex objects. The CSI, like the other spherical representations
of 3-D objects, is defined for convex objects only.
However, many of the concepts defined
mathematically for convex objects are believed to produce good heuristics for non-convex
objects.
This work is being done in collaboration with the Distributed Sensor Systems group at M.I.T.
Lincoln Laboratory.
24.15 Shallow Water Acoustic Inversion
Hertz Foundation Fellowship
National Science Foundation (Grants ECS80-07102 and ECS84-07285)
U.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)
Alan V. Oppenheim, George V. FrisA 28, Michael S. Wengrovitz
The problem of continuous-wave acoustic signal propagation in shallow water is being
investigated. In this environment, components of the acoustic field alternately reflect off both the
28
Woods Hole Oceanographic Institution
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ocean surface and the ocean bottom. In effect, the water can be considered to be an acoustic
waveguide bounded by the ocean surface and the underlying ocean bottom. Several aspects of
this waveguide propagation problem are being studied. The first concerns the development of an
accurate numerical model to predict the magnitude and phase of the acoustic field as a function
of range from the source given the geoacoustic parameters of the water and the bottom. A
technique has been developed which computes the field based on its decomposition into trapped
(resonant) and continuum (non-resonant) components.
A second aspect being studied is the inverse problem. Here, features of the waveguide and the
ocean bottom are desired and measurements of the field over an aperture are given. A parametric
modeling technique has been proposed which reduces the effect of the inherent windowing and
improves the estimate of the bottom reflection coefficient. Another inversion technique has also
been developed which directly computes the sound velocity in the ocean bottom half-space given
measurements of the acoustic field. This technique is based on accurately determining the
branch point of a multivalued function.
The contribution of a branch point is an important component of the signal being processed in
this problem. Current research is directed towards the more general digital signal processing
problem of pole/zero/branch-point modeling.
24.16 Computing the Discrete Hartley Transform
Hertz Foundation Fellowship
National Science Foundation (Grants ECS80-07102 and ECS84-07285)
U.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)
Alan V. Oppenheim, Avideh Zakhor
The discrete Hartley transform (DHT) resembles the discrete Fourier transform (DFT) but is free
from two characteristics of the DFT that are sometimes computationally undesirable. The inverse
discrete Hartley transform is identical to the direct transform and so it is not necessary to keep
track of + i and -i versions as with the discrete Fourier transform. Also, the DHT has real rather
than complex values and thus does not require provision for complex arithmetic or separately
managed storage for real and imaginary parts. The DFT is directly obtainable from the DHT by a
simple additive operation.
We have found an efficient way of computing the Hartley transform which enables us to
compute the DFT with half as many multiplications as the FFT. Wang
and Bracewell 2 have also
found algorithins for the fast Hartley transform. In this research, we will evaluate and compare
these three algorithms in terms of their relative efficiencies. Statistical and deterministic error
properties of these algorithms will also be investigated both theoretically and experimentally.
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References
1. Z. Wang, "Fast Algorithms for the Discrete W Transform and for the Discrete Fourier
Transform," IEEE Trans. Acoust. Speech. Signal Process., ASSP-32, 4, August 1984.
2. R.N. Bracewell, "The Fast Hartley Transform," Proc. IEEE, 72, 8, August 1984.
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